Question 1

The average of class in 35 yr. 6 new students with an average age of 33 yr. joined in that class, there by decreasing the average by half year. The original strength of the class was

Accepted Answer

Let the number of students in the class = N According to the question, (35N + 6 x 33) / (N + 6) = 35 - (1/2) ⇒ 35N + 198 = 34.5 (N + 6) ⇒ 35N +198 = 34.5N + 207 ⇒ 0.5N = 207 -198N = 9/0.5 = 18 ∴ N = 18 days

Question 2

The average age of 5 member of a family is 25 yr. If the servant of the family is included the average age increased by 40% .What is the age of servant?

Accepted Answer

Total age of 5 members = 25 x 5 = 125 yr Total age of 5 member and the servant = (25 + 25 x 40/100) x 6 = 35 x 6 = 210 yr ∴ Age of the servant = 210 - 125 = 85 yr

Question 3

The average age of the 30 woman decreases by 3 month if a new person Priyanka is included in place of 25 yr old woman. Calculate the age of Priyanka.

Accepted Answer

Here, average decreases by 3 months of 3/12 yr. Sum of ages decreased = 30 x 3/12 = 15/2 = 7.5 yr ∴ Age of priyanka = (25 - 7.5) = 17.5 yr.

Question 4

The mean temperature of Monday to Wednesday was 37°C and of Tuesday to Thursday was 34°C. If the temperature on Thursday was 4/5 that of Monday, the temperature of Thursday was

Accepted Answer

Temperature of (Mon + Tue + Wed) = 37 x 3 = 11°C Temperature of (Tue + Wed + Thu) = 34 x 3 = 102°C Temperature of (Mon - Thu) = 111°C - 102°C = 9°C Temperature of [Mon - 4/5(Mon] = 9 Temperature of Monday = 9 x 5 = 45°C ∴ Temperature of Thursday = 45 x 4/5 = 36°C

Question 5

The average of 11 numbers is 36. Out of these 11 numbers, the average of 9 numbers is 34. If the ratio of remaining two numbers is 2 : 3, find out the smaller number.

Accepted Answer

Sum of 11 numbers = 36 x 11 = 396 Sum of 9 numbers = 34 x 9 = 306 Sum of remaining two numbers =396 - 306 = 90 ∴ The smaller number = (2 x 90)/(2 + 3) = 180/5 = 36

Question 6

The average of 5 consecutive old positive integers is 9. The least one amongt them is

Accepted Answer

Let the 5 consecutive positive integers be x + 1, x + 3, x + 5, x + 7, x + 9 Average = (Sum of all terms) / (Number of terms) ⇒ 9 = [(x + 1) + (x + 3) + (x + 5) + (x + 7) + (x + 9)]/5 ⇒ 9 = (5x +25)/5 ⇒ 45 = 5x + 25 ⇒ 5x = 45 - 25 ∴ 5x = 20 ⇒ x = 4 The least one is x + 1 = 4 + 1 = 5

Question 7

The average of the test scores of a class of 'm' students is 70 and that of 'n' students is 91. When the scores of both the classes are combined, the average is 80. What is n/m?

Accepted Answer

According to the question, 70m + 91n = 80 (m + n) ⇒ 70m + 91n = 80m + 80n ⇒ 10m = 11n ⇒ n/m = 10/11

Question 8

If 47a + 47b = 5452, what is the average of a and b?

Accepted Answer

47(a + b) = 5452 ⇒ a + b = 5452/47 = 116 ∴ Average value = (a + b)/2 = 116/2 = 58

Question 9

The average salary per head of all workers of an institution is ₹ 60. The average salary per head of 12 officers is ₹ 400. The average salary per head of the rest is ₹ 56. Then, the total number of workers in the institutions?

Accepted Answer

Let The total number of workers = N According To the question, 60N = 12 x 400 + 56 (N - 12) ⇒ 60N - 56N = 4800 - 672 ⇒ 4N = 4128 ∴ N = 1032

Question 10

Roshan bought 5 pants at ₹25 each, 10 shirts at ₹ 50 each and 15 ties at ₹ 35 each. Find the average price of all the articles.

Accepted Answer

Here, n1 = 5, n2 = 10, n3 = 15, a1 = 25, a2 = 50, a3 = 35 According to the formula, Average price = (n1a1 + n2a2 + n3a3) / (n1 + n2 + n3) = (5 x 25 + 10 x 50 + 15 x 35) / (5 + 10 + 15) = (25 + 100 + 105) / (1 + 2 + 3) = 230/6 = ₹ 38.33

Question 11

The average weight of a class of 15 boys and 10 girls is 38.4 kg. If the average weight of the boys is 40 kg, then what is the average weight of the girls?

Accepted Answer

Given that, number of boys (n1) = 15 Numbers of girls (n2)= 10 Average weight of boys and girls = 38.4 kg Average of boys = 40 kg Let average of girls be a2 By formula, average = (na1 + n2 a2) / (n1 + n2) ⇒ 38.4 = (15(40) + 10 x a2)/(15 + 10) ⇒ 38.4 x 25 = 600+ 10a2 ⇒ a2= (960 - 600)/10 = 360/10 = 36 kg

Question 12

The average marks of 120 students are 35. if the average of passed stuydents was 39. and failed students was 15 then find the number of students who have passed

Accepted Answer

Here n = 120, a = 35, x = 39, y = 15 Number of students passed = n (a - y)/(x - y) = 120(35 - 15)/(39 -15) = 100 students passed

Question 13

A car travels a certain distance from town A to town B at the speed of 42 km/h and from town B to town A at a speed of 48 km/h. What is the average speed of the car?

Accepted Answer

If two equal distance are covered at different speeds at A km/h and B km/h respectively, then Average speed during the whole journey = 2AB/(A + B) km/h ∴ Average speed of the car = (2 x 42 x 48) / (42 + 48) = (2 x 42 x 48)/90 = 44.8 km/h

Question 14

The average of four positive integers is 73.5. The highest integer is 108 and the lowest integer is 29, the difference between the remaining two integers is 15. Which of the following is the smaller of the remaining two integers?

Accepted Answer

Let one integer be x. ∴ Other ingeger x + 15 According to the question, 29 + x + x + 15+ 108 = 4 x 73.5 ⇒ 2x + 152 = 294 ⇒ 2x = 294 - 152 = 142 ⇒ x = 142/2 = 71

Question 15

A cricketer scored some runs in his continuous 9 innings. He scored 100 runs in his 10th innings and increase his average by 8 runs. What was the average of his runs at the end of 10 th innings?

Accepted Answer

Let average of a inning = x Total runs = 9x According to the question, (9x + 100) /10 = x + 8 ⇒ 9x + 100 = 10x + 80 x = 20 Average after 10 inning = 20 + 8 = 28

Question 16

Three year ago, the average age of a family of five members was 27 yr. The present average age is also 27 yr after the inclusion of a child into the family. Find the age of the child.

Accepted Answer

Total age of 5 memeber (3 yr ago) = 27 x 5 = 135 yr Total age of 5 members (at present) = 135 + 5 x 3 = 150 yr. Let the persent age of child = x ∴ 27 = (150 + x)/6 ⇒ x = 162 - 150 = 12 yr.

Question 17

The average age of three boys is 15 yr. If the ratio of their ages is 3 : 5 : 7, What is the age of the oldest boy?

Accepted Answer

Total age of all three boys = 3 x 15 = 45 yr Ratio of ages = 3 : 5 : 7 ∴ Age of the oldest boy = [7/(3 + 5 + 7)] x 45 = (7/15) x 45 = 21 yr

Question 18

Nine friends have dinner in a hostel. Eight of them spent ₹ 12 each on their meals and the ninth spent ₹ 16 more than the average expenditure of all the nine. Find out the total money spent by them?

Accepted Answer

Let average expenditure of 9 persons = x. According to the question, 12 x 8 + (x + 16) = 9x ⇒ 8x = 112 ⇒ x = 112/8 = 14 ∴ Total money spent = 9x = 9 x 14 = ₹ 126

Question 19

In a certain examination, the average marks of an examinee is 64 per paper. if he had obtained 18 more marks for his Mathematics paper and 4 more marks for his English paper, his average per paper would have been 66. How many papers were there in th…

Accepted Answer

Let the number of papers = x. According to the question, 64x + 18 + 4 = 66x ∴ 2x = 22 ∴ x = 22/2 = 11

Question 20

The average markes obtained by 120 students in an examination is 30. if the aveage marks of passed students is 40 and that of the failed students is 10. what is the 25% of the number of students who passed the examination?

Accepted Answer

Let number of passed students = N Total marks = 120 x 30 According to the question, 40N + (120 - N) x 10 = 120 x 30 ⇒ 3600 = 40N + 1200 - 10N ⇒ 30N = 2400 ∴ N = 2400/30 = 80 ∴ 25% of 80 = 80/4 = 20

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